Mathematical Aspects of
Intravenous Therapy
Simon Shah
Pharmacy Department
General Points







Use S.I. units at all times
Grams (g)
Milligrams (mg)
Micrograms
Nanograms
Litres (l)
Millilitres (ml)
Units





1kg contains 1000g
1g contains 1000mg
1mg contains 1000 micrograms
1 microgram contains 1000 nanograms
1l contains 1000ml
Concentrations






Different ways of expressing
concentration:
Weight in volume
Units in volume
Percentages
Molar
Ratios
Weight in Volume
Expressed as - grams/litre (g/l)
mg/ml
 e.g. dobutamine 250mg/5ml
 digoxin 0.5mg/2ml
 morphine 10mg/ml
 pethidine 50mg/ml or 100mg/2ml
Units in Volume



Unit is a measure of biological activity
i.e. 1 unit heparin is not equal to 1 unit of
insulin.
Insulin 100 units/ml
Heparin 1000 units/ml
5000 units/ml
5000 units/0.2ml
Percentages



1%w/v = 1g in 100ml (1000mg in 100ml)
5%w/v = 5g in 100ml (or 50g/l)
0.9%w/v = 900mg in 100ml (or 9g/l)
Potassium Chloride
15%w/v = 15g/100ml = 1.5g/10ml
10ml also contains 20mmol
Molar
Rarely used
 1 molar = 1mole/litre
 1 mole contains a certain number of
molecules, electrolytes etc.
 1 molar solution = 1000mmol/l
Often used by Biochemistry to report results
e.g. Na 139 mmol/l

Ratio

Concentrations expressed as 1 in..... means
1g in however many mls
1 : 1 solution contains 1g/ml
1 : 1000 is 1/1000th of this

Adrenaline





1 : 1000 = 1g/1000ml or 1mg/ml
1 : 10,000 = 1g/10,000ml or 1mg/10ml
Exception –Tuberculin -ratio based on units
Other points

Always make sure decimal points are
preceded by a number



e.g. 0.5mg not .5mg
Always think carefully about calculations
Always get a check on calculations
Calculations - Volumes

Volume required is based on proportions.
What you want (Dose) x Volume you have(ml)
What you have (Amount in vial)
e.g. morphine 10mg/ml. Dose required = 15mg
Volume required = 15mg x 1ml = 1.5ml
10mg
Gentamicin 80mg in 2ml


Dose prescribed is 140mg
What volume do you need?
You want 140mg x It is in 2mls
You have 80mg
= 3.5ml
Aminophylline 250mg in 10ml


Dose prescribed is 210mg
What volume is required?
You want 210mg x it is in 10ml
You have 250mg
= 8.4ml
Infusions
Giving IV drugs by infusion requires
two separate stages:


Preparation
Administration
Infusions - Doses
Dose of a drug given will depend on two
factors:
1. Concentration of infusion (mg/ml)
2. Rate of administration (ml/hr)
BOTH must be known for the dose to be
calculated.

e.g. 2ml/hr on a prescription means
nothing.
Infusion Preparation
Two main methods:
Amount of drug added individualised to
patient
2. Standardised solutions
1.
Individualised Infusions
AMINOPHYLLINE INFUSION
(Vials available as 250mg/10ml)
A 60kg patient is to receive an aminophylline
infusion at a rate of 0.5mg/kg/hr for 24
hours
How much aminophylline injection
(250mg/10ml) would you add to 1L of fluid
and what rate would you set the pump at?
0.5mg/kg/hr = 30mg/hr = 720mg in 24 hrs
720 x 10 = 28.8ml
250
Add 28.8ml to 1L infusion fluid
1 litre over 24 hours = 42ml/hr
Standard Solution Infusions
AMINOPHYLLINE INFUSIONStandardised solution.
e.g. 500mg in 500ml, i.e. 1mg/ml
Dose is 30mg/hr therefore rate is 30ml/hr


Easier to adjust rate if dose changes
Standardisation of preparation between
nurses
Dobutamine 250mg in 5ml
A 60kg patient is currently receiving
dobutamine at a rate of
8 micrograms/kg/min...
How would you prepare the solution
 at what rate would you set the syringe
pump?
Use a standard solution = 250mg/50ml


Standard solution preparation 250mg/50ml
Dose
= 60 x 8 = 480 micrograms/minute
= 480 x 60 = 28,800 micrograms/hour
= 28,800/1000mg/hour
= 28.8mg/hr

Dose = 28.8mg/hour

Infusion Concentration = 250mg in 50ml

Rate = 28.8mg/hour x 50ml = 5.8ml/hr
250mg
i.e. the rate you want (mg/hr) x volume it’s in (ml)
the amount you have (mg)
Adrenaline 1:1000


How would you prepare a 50ml infusion of
adrenaline 0.2mg/ml
it needs to be added to a 50ml syringe
Amount = Concentration x Volume
= 0.2mg/ml x 50ml = 10mg in 50ml
= 10ml of 1:1000 (1mg/ml)
Glyceryl Trinitrate 50mg/10ml
How would you prepare a 0.1mg/ml infusion
of GTN?
 needs to be added to a 500ml polyfusor
Amount = Concentration x Volume
= 0.1mg/ml x 500ml
= 50mg in 500ml polyfusor
= 1 x 10ml ampoule

Heparin



Heparin is to be given at a dose of 30,000
units/day
How would you prepare the solution and
what rate would you use?
Use a 1000unit/ml solution e.g. Pump-Hep





Use a 1000unit/ml solution
Draw up 30ml into syringe. Don’t dilute.
30,000 units/24 hours = 1250 units/hour
1250 units = 1.25ml therefore rate = 1.25
or 1.3ml/hr
What if the dose is increased to
40,000 units/day?
Summary







Different units may be used
Different uses of same calculation
Doses depend on concentration and rate
Use standard solutions if possible
Calculate carefully
Get a check - redo calculation
If not sure - Ask!